PREPARATION: To roast beet, heat oven to 350 degrees. Place the beet in the center of a square of tin foil, sprinkle with olive oil, add thyme, and season with salt. Fold the foil into a package and place on a sheet pan. Bake 1 to 2 hours. Check beet by piercing with a knife. There should be no resistance. If there is, cook longer. Take the beet out, let cool, and cut into small dice.

To poach the eggs, take a 2-quart pan and fill three-fourths with water. Season water with salt. Bring to a hard simmer, not boiling too hard. Crack one egg into a bowl. Give the water a slight stir with a spoon and slip egg into the water. The swirling water will help wrap the egg white around the egg. Poach 3 minutes and use a slotted spoon to lift the egg from the poaching liquid. Repeat for other three eggs.

To cook mushrooms, mince shallot in a 7-inch pan, heat about 1 tablespoon olive oil over medium heat. Add shallots and cook 30 seconds. Add mushrooms and cook over medium to medium low heat. Shiitake mushrooms do not do well on high heat. It is preferred to cook them slowly. Adding a bit of chicken stock and essentially poaching them keeps them from drying out. Season with salt and pepper and cook for no longer than 1 1/2 minutes. Remove to a plate.

Drizzle some olive oil and rice vinegar onto the greens. Season with a pinch of salt (a step most people don't do but a step that will make all the difference in the finished product). Pepper to taste. Toss salad.

Place some salad on a plate. Sprinkle beets and mushrooms over salad. Place poached egg on top. Drizzle olive oil on egg and a crack of pepper.